Question

89 and a = 6. Suppose a simple random sample of size n = 36 is obtained from a population with (a) Describe the sampling distribution of x. (b) What is P (x >90.65) ? (c) What is P (xs 86.85) ? (d) What is P (87.9<x<90.9) ? Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). (a) Choose the correct description of the shape of the sampling distribution of O A. The distribution is skewed left. O B. The distribution is uniform O C. The distribution is skewed right. OD. The distribution is approximately normal O E. The shape of the distribution is unknown. Find the mean and standard deviation of the sampling distribution of x. Click to select your answer(s). ON w А N

Answer 1

Given, Sample size = n = 36 M = 89 r = 6 a) The Shape of the sampling distribution D. The distribution - nommal. is appaimately be the mean and standasd deviation of the sampling distribution of Ž is Mx = M = (891

b> p (=>90.65) = p/x-M 90.65-89 1 According 136 to central limit theorem = P (Z > 1.65) =I-P(Z <1.65) using 2-table, we get = 1-0.9505 : P(x>90.65) = 10.0495 -

c> P ( x < 86.85) = p/x-M 286.85-89 According to central limit theores =P(Z <-2.15) using 2-table, we get p (8386.85) = 0.0158

dy P( 87.9 < X <90.g) -p/87.9-M X-M 9o.g-M According to central limit theorem. =P(87.9-89 <zc 90.9-89 16 √36 136 =P(-1.10 cz <1.90 = P12<1.90) - Plz<-1.10) using z-table, we get = 0.9713-001357 P(87.9<x<go.g) -